incompatible vs like chalk and cheese

incompatible

adj
  • Of two things: that cannot coexist; not congruous because of differences; unable to function together due to dissimilarities. 

  • Incapable of being together without mutual reaction or decomposition, as certain medicines. 

noun
  • An incompatible substance; one of a group of things that cannot be placed or used together because of a change of chemical composition or opposing medicinal qualities. 

  • A consequent of a contrary. 

like chalk and cheese

How often have the words incompatible and like chalk and cheese occurred in a corpus of books? (source: Google Ngram Viewer )